Using a one-parameter model to sequentially estimate the root of a regression function. (Q1583204)

This paper considers sequential estimation of the root of a regression function. We explore the possibility of using a one-parameter model to fit data that is collected sequentially and then calculate the value of the design variable for the next observation. This design value itself can serve as an estimator of the root. We find that when the design variable has continuous values, our estimates are consistent. However, when the design variable has discrete values, there are situations in which the estimates can get `stuck' at the wrong value and the method then fails to converge to the correct point. Nonetheless, under certain conditions, we can establish the consistency of the estimates even if the design variable is discrete.